Ans: sanity testing is nothing but before going test the 
entire application we have to test whether the application 
is stable(all functionalites are working properly to go for 
system testing) or not. If the application is we go for 
further testing otherwise we reject the build submit issues 
where as regression testing each version of the build 
verified and submitted defects to the development team then 
we test the application with selected test cases whether 
the system reflected with any modifications.

Open the Ellamey.com page. See the Functional Requirements
are present on the page r not according to the client
requirement.check all the module pages.This type of checking
called sanity testing.If search button is displaying in the
page then it is sanity testing. then check the functionality
is working then it is smoke testing.

Now regression.
Suppose u have Modules  A,B,C,D.u checked all the modules
and u prepared the testcases.NOw u r client asked to add F
module in the Middle of B and C.So after developing the E
module From the Development Team,The E module is Integrated
between B and C.Now the Total Module Flow is ABECD.
Now u have 2 check that after integrating E module,Any
effect on A,B C D modules.Sometimes Some Effect will be
appear to the Remaining module.Then u have 2 check all the
Modules again,Prepare testcases.Then u have 2 compare the
Old testcases with New Testcases.
This is Regression Testing.

Hai Chennamsubbaraidu Plz give me one clarification in the 
above answer.
This is from the above example continuation, Sometimes Some 
Effect will be appear to the Remaining module.Then u have 2 
check all the Modules again,Prepare testcases.Then u have 2 
compare the Old testcases with New Testcases.
This is Regression Testing.
     Here my clarification is Actually in A,B,C,D Modules 
we wrote the test cases and completed the build up to 
that.Then we are adding the Module E in in-between the 
Modules B and C, then we have to test the Modules B and E + 
E and C because there will be no effect between Modules A 
and B + C and D. And whether we have to write testcases for 
all the modules if one Module is added in between A,B,C,D 
Modules.
 My name is BapiRaju, Plz see to my clarification and send 
the response very urgently******
              My eid is <bapiraju_ka@yahoo.com>

Good Question.See Maximum for A Module and D module there
will be no effect.Sometimes there will be effect.While u r
working on the project u will come to know ,whether any
effect to application or not.coz before 2 months i worked
for one Project.In that Project i faced the problem.So it be
better to do test for all modules.As the Tester
Responsibility is to give the Good Product.So it is
Mandatory to check.

If u have any doubts ,Feel Free to Ask.

sanity testing: whether build is stable for conducting 
testing or not

Regression Testing: which test a system once again to 
ensure that a functions as expected as per the 
specifications or its requirements.
or
executing the test cases on modified form of build

Sanity Testing: Whether the build is stable to test or not.

Regression Testing: Re execution of the test cases on 
modified build is called Regression testing.